Matrices Test -...

If $$\mathrm{A}=\left(\begin{array}{lll}
x & 1 & 4\\
-1 & 0 & 7\\
-4 & -7 & 0
\end{array}\right)$$ such that $$\mathrm{A}^{\mathrm{T}}=-\mathrm{A}$$, then $$\mathrm{x}=$$

$$\mathrm{If}\mathrm{A}=\left[\begin{array}{lll}
2 & x-3 & x-2\\
3 & -2 & -1\\
4 & -1 & -5
\end{array}\right]$$ is a symmetric matrix then $$\mathrm{x}$$

$$A=\left[\begin{array}{ll}
2 & 1\\
3 & 0
\end{array}\right]$$ then $$\mathrm{A}^{2}+2\mathrm{A}+I=$$

$$A=\begin{bmatrix} 1 & 2 & 1 \\ 0 & 1 & -1 \\ 3 & -1 & 1 \end{bmatrix}$$  then $$A^{2}-A=$$

$$\begin{bmatrix} 10 & 20 & 30 \\ 20 & 45 & 80 \\ 30 & 80 & 171 \end{bmatrix}=\begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 4 & 1 \end{bmatrix}\begin{bmatrix} x & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 1 \end{bmatrix}\begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \end{bmatrix}$$ then $${x}=$$

lf $$ \left[3x^{2}+10xy+5y^{2} \right]=\begin{bmatrix}x & y \end{bmatrix}A\begin{bmatrix} x\\ y\end{bmatrix}$$, and $${A}$$ is a symmetric matrix then $$\mathrm{A}=$$

$$1\mathrm{f}\mathrm{A}=\left[\begin{array}{lll}
4 & 1 & 0\\
1 & -2 & 2
\end{array}\right],\ \mathrm{B}=\left[\begin{array}{lll}
2 & 0 & -1\\
3 & 1 & 4
\end{array}\right]$$, $$\mathrm{C}=\left[\begin{array}{l}
1\\
2\\
-1
\end{array}\right]$$ and $$(3\mathrm{B}-2\mathrm{A})\mathrm{C}+2\mathrm{X}=0$$ then $$\mathrm{X}$$ is equal to

$$A=\begin{bmatrix} 1 & -3 & -4 \\ -1 & 3 & 4 \\ 1 & -3 & -4 \end{bmatrix}$$ and $$\mathrm{A}^{2}=\lambda I$$ then $$\lambda=$$

$$A=\left[\begin{array}{lll}
2 & 2 & 1\\
1 & 2 & 1\\
3 & 4 & 2
\end{array}\right]$$ then ($$\mathrm{A}-\mathrm{I}$$) $$(\mathrm{A}-2I)=$$

lf  $$A=\begin{bmatrix} 1 & 2 & 1 \\ 3 & 4 & 2 \\ 1 & 3 & 2 \end{bmatrix}$$ and $$ B=\begin{bmatrix} 10 & -4 & -1 \\ -11 & 5 & 0 \\ 9 & -5 & 1 \end{bmatrix}$$ then